Bubbling solutions for nonlocal elliptic problems
We investigate bubbling solutions for the nonlocal equation Aω s u = up, u > 0 in ω, under homogeneous Dirichlet conditions, where ω is a bounded and smooth domain. The operator As ω stands for two types of nonlocal operators that we treat in a unified way: either the spectral fractional Lapl...
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todo:paper_02132230_v33_n2_p509_Davila2023-10-03T15:10:06Z Bubbling solutions for nonlocal elliptic problems Dávila, J. López Ríos, L. Sire, Y. Dirichlet problem Fractional Laplacian Stable critical points Sub and supercritical exponents We investigate bubbling solutions for the nonlocal equation Aω s u = up, u > 0 in ω, under homogeneous Dirichlet conditions, where ω is a bounded and smooth domain. The operator As ω stands for two types of nonlocal operators that we treat in a unified way: either the spectral fractional Laplacian or the restricted fractional Laplacian. In both cases s ∈ (0, 1), and the Dirichlet conditions are different: for the spectral fractional Laplacian, we prescribe u = 0 on ∂ω, and for the restricted fractional Laplacian, we prescribe u = 0 on ℝn\\ω. We construct solutions when the exponent p = (n+2s)/(n-2s)±ϵ is close to the critical one, concentrating as ϵ → 0 near critical points of a reduced function involving the Green and Robin functions of the domain. © European Mathematical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02132230_v33_n2_p509_Davila |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Dirichlet problem Fractional Laplacian Stable critical points Sub and supercritical exponents |
| spellingShingle |
Dirichlet problem Fractional Laplacian Stable critical points Sub and supercritical exponents Dávila, J. López Ríos, L. Sire, Y. Bubbling solutions for nonlocal elliptic problems |
| topic_facet |
Dirichlet problem Fractional Laplacian Stable critical points Sub and supercritical exponents |
| description |
We investigate bubbling solutions for the nonlocal equation Aω s u = up, u > 0 in ω, under homogeneous Dirichlet conditions, where ω is a bounded and smooth domain. The operator As ω stands for two types of nonlocal operators that we treat in a unified way: either the spectral fractional Laplacian or the restricted fractional Laplacian. In both cases s ∈ (0, 1), and the Dirichlet conditions are different: for the spectral fractional Laplacian, we prescribe u = 0 on ∂ω, and for the restricted fractional Laplacian, we prescribe u = 0 on ℝn\\ω. We construct solutions when the exponent p = (n+2s)/(n-2s)±ϵ is close to the critical one, concentrating as ϵ → 0 near critical points of a reduced function involving the Green and Robin functions of the domain. © European Mathematical Society. |
| format |
JOUR |
| author |
Dávila, J. López Ríos, L. Sire, Y. |
| author_facet |
Dávila, J. López Ríos, L. Sire, Y. |
| author_sort |
Dávila, J. |
| title |
Bubbling solutions for nonlocal elliptic problems |
| title_short |
Bubbling solutions for nonlocal elliptic problems |
| title_full |
Bubbling solutions for nonlocal elliptic problems |
| title_fullStr |
Bubbling solutions for nonlocal elliptic problems |
| title_full_unstemmed |
Bubbling solutions for nonlocal elliptic problems |
| title_sort |
bubbling solutions for nonlocal elliptic problems |
| url |
http://hdl.handle.net/20.500.12110/paper_02132230_v33_n2_p509_Davila |
| work_keys_str_mv |
AT davilaj bubblingsolutionsfornonlocalellipticproblems AT lopezriosl bubblingsolutionsfornonlocalellipticproblems AT sirey bubblingsolutionsfornonlocalellipticproblems |
| _version_ |
1807323825178673152 |